 Fermion-to-boson thermal integral ratio

For $s>0$,This follows from $(e^x+1{)}^{-1}=(e^x-1{)}^{-1}-2(e^{2x}-1{)}^{-1}$. In three spatial dimensions it gives the fermion-to-boson ratios $3/4$ for ultrarelativistic particle number and $7/8$ for energy density.